Answer:
SOLVE A SYSTEM OF LINEAR EQUATIONS BY GRAPHING.
Graph the first equation.
Graph the second equation on the same rectangular coordinate system.
Determine whether the lines intersect, are parallel, or are the same line.
Identify the solution to the system. ...
Check the solution in both equations.
Step-by-step explanation:
An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are linear equations in two variables.
Find the product.
(6t²-8bs) (t² + bs)
Enter the correct answer.
The product of given equation is [tex]6t^{4} + 6t^{2} bs-8bst^{2} -8b^{2} s^{2}[/tex] .
Define expression.Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
[tex]=(6t^{2} -8bs) (t^{2} + bs)[/tex]
[tex]=6t^{2} (t^{2} + bs) -8bs(t^{2} + bs)[/tex]
[tex]=6t^{4} +6t^{2}bs -8bst^{2} -8b^{2} s^{2}[/tex]
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Jake has a floor that is 64 square feet. He wants to tile the entire floor using large tiles that measure 3 feet by 5 feet. The tiles may be cut as needed. What is the fewest number of tiles required to fill the space while also requiring the fewest tiles to be cut? Show a diagram of the completed floor.
The number of tiles required to fill the space while also requiring the fewest tiles to be cut is 5 .
What is area ?
Area can be defined as the total space taken by a 2-dimensional surface or shape of an object.
Given
Jake has a floor that is 64 square feet.
He wants to tile the entire floor using large tiles that measure 3 feet by 5 feet.
The area of 3 feet by 5 feet could be = 3 * 5 = 15 square meters.
number of tiles required to fill the space could be = 64 / 15
that is 4.3 (approx )
Hence , the number of tiles required to fill the space while also requiring the fewest tiles to be cut is 5 .
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Anything would be greatly appreciated!!
As seen in the illustration, the polygon's surface area is 12 + 4√5 square units.
What is meant by polygon's surface area?The region that a particular polygon occupies in a two-dimensional plane, whether it be a triangle, square, quadrilateral, rectangle, parallelogram or rhombus, hexagon or pentagon, is defined as its area. Depending on how they are shaped, different types of polygons have different areas or formulas for areas. One way to think of a polygonal surface is as a surface made up of polygonal faces. All of the polygons must belong to the same type (triangles, quadrilaterals or whatever). The user must ensure that each polygon's vertices all sit in a plane if the polygons are of a higher order than triangles. The collection of polygons or faces collectively make up the object's "skin." A wide range of solids and surfaces can be graphically represented using this technique.Therefore the correct option is C) 12 + 4√5 square unit
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suppose you have a credit card debt of $6000. Last month, the bank charged you $55 interest on the debt. The solution to the equation 55= 6000/12 * r represents the annual interest rate in the credit card, r. Find the annual interest rate on the credit card
Answer: The formula for the interest charged on a credit card debt is:
Interest = (Principal * Annual Interest Rate) / 12
We know that the interest charged last month is $55, and the principal (the credit card debt) is $6000, so we can substitute these values into the formula and solve for the annual interest rate:
55 = (6000 * r) / 12
To find the annual interest rate, we will solve for r.
r = (55 * 12) / 6000
r = 0.09 which is a 9% annual interest rate.
So, the annual interest rate on the credit card is 9%.
Step-by-step explanation:
Which property of equality illustrates the statement "If AC = 14, then BD + AC = BD + 14?"
A. Transitive Property of Equality
B. Symmetric Property of Equality
C. Division Property of Equality
D. Substitution Property of Equality
'Substitution Property of Equality' illustrates the statement "If AC = 14, then BD + AC = BD + 14" from the question.
What is property of equality?
The equality characteristics define the relationship between two equal quantities. If a mathematical operation is applied to one side of an equation, it must also be applied to the opposing side to keep the equation balanced.
The Substitution Property of Equality states that if we know that two expressions are equal, we can substitute one of them for the other in any equation.
In this statement, it is stated that "If AC = 14, then BD + AC = BD + 14." Here we substitute 14 for AC in BD + AC = BD + 14. Which means that if we know that AC = 14, we can substitute 14 for AC in any equation, and the equation will still be true.
Therefore, given statement illustrates the Substitution Property of Equality.
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Ashley and Saskia each think of a number.
1 less than Ashley's number is equal to 3 lots of Saskia's number.
4 lots of Ashley's number added to Saskia's number is 95.
Using the information above, write and solve two simultaneous equations to work out Ashley's and Saskia's numbers.
Based on the the information provided above, Ashley's and Saskia's numbers are equal to 22 and 7 respectively.
How to work out Ashley's and Saskia's numbers?In order to write a system of equations to describe this situation, we would assign variables to Ashley's number and Saskia's number respectively, and then translate the word problem into an algebraic equation as follows:
Let the variable x represent Ashley's number.Let the variable y represent Saskia's number.Translating the word problem into an algebraic equation, we have the following:
x - 1 = 3y .....equation 1.
4x + y = 95 .......equation 2.
Making x the subject of formula in equation 1, we have:
x = 3y + 1 .......equation 3.
Substituting equation 3 into equation 2, we have:
4(3y + 1) + y = 95
12y + 4 + y = 95
13y = 95 - 4
13y = 91
y = 91/13
y = 7.
For the value of x, we have:
x = 3y + 1
x = 3(7) + 1
x = 21 + 1
x =22.
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A principal of $3600 is invested at 3.5% interest, compounded annually. How much will the investment be worth after 12 years? Use the calculator provided and round your answer to the nearest dollar. X S
Answer:
$5043
Step-by-step explanation:
To find the value of the investment after 12 years, you can use the following formula:
A = P * (1 + r/n)^(nt)
Where:
A = final amount
P = principal
r = interest rate
n = number of times the interest is compounded per year
t = number of years
Plugging in the values from the problem, we get:
A = 3600 * (1 + 3.5/100)^(1*12)
Solving this equation, we get:
A = $5043.33
So, after 12 years, the investment will be worth $5043.33.
how to horizontally stretch a cubic fucnction
Answer:
Steps for How to Transform the Graph of a Cubic Function
Step 1: The standard form of a cubic function is y=a(x−h)3+k y = a ( x − h ) 3 + k , where a indicates a stretch or a shrink, h indicates a vertical shift, and k indicates a horizontal shift.
Step-by-step explanation:
Convert:
30 quarts
=
bushels
Round to the nearest hundredths.
Answer:
30 quarts= 0.8057 bushels
rounded to the nearest hundredths = 0.81
100° хо 100%
what is the answer for x?
The answer of x is 100 degree.We can find by using percentage formula.
What do we mean by percentage?Percentage is a value or ratio that shows a fraction of 100. Percent means per 100. It does not have any units.If we have to calculate percent of a number then we divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
What is the percentage formula?The formula used to calculate percentage is: (value/total value)×100%.The most basic application of percentages is to compare one quantity against another. When we want to talk about data in this way we use it with the word, "of." To use this data as an example, we would say, for example, "25% of people prefer cake," as in this example.
Now we have
100 = x of 100%
100= x * 100/100
100= x
Hence we can calculate value of x.
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(2x+1)(x-3)(x+5) expand and fully simplify
Answer:
2x^3+5x^2−28x−15
Step-by-step explanation:
Goran wants to build a square frame with sides that are 5.25 inches long. Natalie wants to build a square sandbox and needs 11 times the amount of wood that Goran needs to build his frame. They have 4 pieces of wood that are each 65.5 inches long. How much wood will they have left over after making the frame and sandbox?
A square is a two-dimensional closed shape with 4 equal sides and 4 vertices. Its opposite sides are parallel to each other. We can also think of a square as a rectangle with equal length and breadth.
What is a square?The wood left over after making the frame and the sandbox is 10 inches.A square is a two-dimensional figure that has four sides and all four sides are equal.Definition. Square is a regular quadrilateral, which has all the four sides of equal length and all four angles are also equal. The angles of the square are at right-angle or equal to 90-degrees. Also, the diagonals of the square are equal and bisect each other at 90 degrees.A square is a four-sided figure whose sides are all the same length and whose angles are all right angles measuring 90 degrees.Square is slang for a person who is conventional and old-fashioned, similar to a Fuddy-duddy. This sense of the word "square" originated with the American jazz community in the 1940s, in reference to people out of touch with musical trends.The area of a square is given as side².
We have,
The total amount of wood.
= 4 x 65.5
= 262 inches.
Frame:
Side = 5.25 inches
The perimeter of the frame.
= 4 x 5.25
= 21 inches
Now,
Sandbox:
The wood used for the sandbox.
= 11 x 21
= 231 inches
The remaining wood.
= 262 - (21 + 231)
= 262 - 252
= 10 inches
Thus,
The remaining wood is 10 inches.
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Question 1-1
Barrett earns $15 per hour cutting grass and $10 per hour tutoring reading. In one month, Barrett needs to save at least $400 for a
new lawnmower but does not want to work more than 35 hours.
Part A: Let z represent the hours cutting grass and y represent the hours tutoring. Given z 20 and y ≥ 0, select all the inequalities
that represent the situation.
On solving the inequality we know, Barrett should work 25 hours tutoring and 10 hours cutting grass to make $400.
What exactly does inequality mean?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality results from a lack of balance.
Solution:-
given,
z=hours of cutting grass
y=hours of tutoring
Two equation can be made using given condition
15z+10y=400
and
z+y=35
Solving both equation simultaneously,
we get
y=25
z=10
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Fill in the blanks below in order to justify whether or not the mapping shown represents a function. Set A 5 0 7 Set B -2 9 -1 -3 The mapping diagram above a function since in where there .
The mapping does not represents a function
How to identify a function?A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input
In this case, for the mapping represent a function, every element in set A must be mapped to exactly one element in set B.
Since there is more than one arrow from set A (5) pointing to different values in set B (-2 and 9), then it is not a function. Also, the two different value (5 and 7) in set A has the same value (-2) in set B.
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ln 4 - ln x = 2
Solve for x
Show all steps
Answer:
To solve this equation, we first need to isolate the ln term on one side of the equation. To do this, we can subtract ln 4 from both sides to get:
ln 4 - ln x - ln 4 = 2 - ln 4
This simplifies to:
-ln x = 2 - ln 4
Next, we can add ln 4 to both sides to get:
-ln x + ln 4 = 2
This simplifies to:
ln 4 - ln x = 2
Now, we can apply the identity ln a - ln b = ln(a/b) to both sides of the equation to get:
ln(4/x) = 2
To solve for x, we can apply the inverse logarithm function (exp) to both sides:
4/x = exp(2)
This simplifies to:
x = 4/exp(2)
Finally, we can evaluate this to get the value of x:
x = 4/exp(2) = 4/7.38905609893065
So the solution is x = 4/7.38905609893065.
Step-by-step explanation:
Which of the following has kinetic energy?
O A. Food
O.B. Motion
OC. Gravity
OD. Light
Answer:
light
Step-by-step explanation:
it has kinetic energy
Answer:
Step-by-step explanation: Kinetic energy is made because of movement. So Motion would be the correct answer
evaluate - [tex]6^{2}- 2(5+1+3[/tex]
The expression 6² - 2(5 + 1 + 3) after evaluation gives 18.
What is BODMAS rule?BODMAS rule is rule for operation of numbers in a specific order when more than one type of operations is involved.
BODMAS is the abbreviated form for Brackets, Order including powers and exponents, Division, Multiplication, Addition and Subtraction.
Given expression is, 6² - 2(5 + 1 + 3).
First we should do the operation in brackets.
6² - 2(5 + 1 + 3) = 6² - 2 (9)
Now we should do the power operations.
6² - 2 (9) = 36 - 2 × 9
Now we do multiplication.
36 - 2 × 9 = 36 - 18
Now we do subtraction.
36 - 18 = 18
Hence the answer of the expression given is 18.
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hello i neeed help with my math question 5
Answer:
Add a file to it.
Step-by-step explanation:
We can't see anything.
Polynomial in standard form
1.
7-3x^3+6x^2
2.
2y-3-8y^2
Answer:
[tex]-3x^3+6x^2+7[/tex][tex]-8y^2+2y-3[/tex]Step-by-step explanation:
The terms are ordered from greatest to least degree.
What's the inches equivalent of 63.5 millimeters? A. 2.5, B. 24, C. 3.2. D 31
Answer: A
Step-by-step explanation: 2.5 inches = 63.5 millimeters
Lisette wrote the following algebraic expression to represent “4 times as large as the product of w and 11.”
The translation of the sentence "4 times as large as the product of w and 11" to an expression is 44w
How to translate the algebraic sentence to an expressionFrom the question, we have the following parameters that can be used in our computation:
“4 times as large as the product of w and 11.”
The number is represented with w
So, the statement remains unchanged as follows
“4 times as large as the product of w and 11.”
4 times as large means 4 *
So, we have the following representation
4 times as large as the product of w and 11 ⇒ 4 * the product of w and 11.
the product of means that we multiply
4 times as large as the product of w and 11 ⇒ 4 * w * 11
Evaluate the products
This gives
4 times as large as the product of w and 11 ⇒ 44w
Hence, the expression is 44w
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Bob's Gift Shop sold 550 cards for Mother's Day. One salesman, Anand, sold 4% of the cards sold for Mother's Day. How many cards did Anand sell?
22 cards were sold by the Anand.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that Bob's Gift Shop sold 550 cards for Mother's Day.
One salesman, Anand, sold 4% of the cards sold for Mother's Day.
We need to find the number of cards sold by Anand
Convert 4% to decimal by dividing 4 by 100
4/100=0.04
Now multiply 0.04 with 550
0.04×550
22
Hence, 22 cards were sold by the Anand.
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3x+1
1. A function f: x →
X-1
(i)
Find the images of -1 and 3.
(ii)
Find the value of x for which f(x) = 7
2. The set P = {-2,-1,0,1,2} maps onto Q by the function f(x)=x²-2, where x E P.
(i)
Find the elements of Q.
(ii)
3. Given that f(x) = 2x - 1 and g(x) = x² +1:
Find f(1 + x):
Find the range of values of x for which f(x) < -3;
Simplify f(x) - g(x).
(i)
(ii)
(iii)
,x # 1, is defined on the set (-1, 0, 2, 3, 4, 5)
Draw a diagram showing the mapping between P and Q.
(i)
4. The function f and g are defined as follows: f:x →→ 2
x-1 and g:x→ 3x + 1
Evaluate f(-) +1
(ii)
Solve f(x) = g(-2)
5. Given that f(x) = px + q, find the values od p and q, if f(2)= 4 and f(4) == 10
The function f is defined as f:x→ 3x² - 5x.
6.
(i)
Evaluate f(--3)
(ii)
7. The functions f and g are defined as: f:xx-2 and g: x2x²-1. Solve:
(i) f(x) = g(-²/-) (ii) f(x) + g(x)= 0
4
Find the values of x for which f(x) = -² 3
On solving the provide the question, we can say that - the value of the following function is f(x) = -5x - 1.
what is function?The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.
[tex]x = -2, y = 9; x = -1 , y = 4; x =0, y = -1.[/tex]
x = 0 , y = -1 so c = -1.
slope of line [tex]= (4-9) / (-1-(-2)) = -5/ 1 = -5.[/tex]
function f(x) = -5x - 1.
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Answer:
Step-by-step explanation:
1. (i) f(-1) = 3(-1) + 1 = -2 and f(3) = 3(3) + 1 = 10
(ii) To find the value of x for which f(x) = 7, we can set f(x) equal to 7 and solve for x:
3x + 1 = 7
3x = 6
x = 2
2. (i) Q = {x² - 2 | x E P} = {(-2)² - 2, (-1)² - 2, (0)² - 2, (1)² - 2, (2)² - 2} = {4, 0, -2, -1, 2}
(ii) As f(x)=x²-2, and P = {-2,-1,0,1,2} mapping into Q is {-2,-1,0,1,2} to {4,0,-2,-1,2}
3. (i) f(1 + x) = 2(1 + x) - 1 = 2x + 1
(ii) To find the range of values of x for which f(x) < -3, we can set f(x) equal to -3 and solve for x:
2x - 1 < -3
2x < -2
x < -1
so x can be any value less than -1
(iii) f(x) - g(x) = (2x - 1) - (x² + 1) = 2x - x² - 2
4. (i) f(-1) + 1 = 2(-1) - 1 + 1 = -1
(ii) To solve f(x) = g(-2), we can substitute the expressions for f(x) and g(x) into the equation:
2x - 1 = 3(-2) + 1
2x - 1 = -5
2x = -6
x = -3
5. f(x) = px + q, given that f(2)= 4 and f(4) == 10
so
4 = 2p + q
10 = 4p + q
solving for p and q we get p = 3 and q = -2
6. (i) f(--3) = 3(-3)² - 5(-3) = -27
7. (i) To solve f(x) = g(-2/-4), we can substitute the expressions for f(x) and g(x) into the equation:
x-2 = (1/4)x² - 1
x-2 = x²/4 - 1
4x-8 = x²-4
x²-4x+4 = 0
x = 2, -2
(ii) To solve f(x) + g(x) = 0
x-2 + x²-1 = 0
x²-2x+1 = 0
(x-1)² = 0
x = 1
for f(x) = -² 3 the expression does not make sense, but assuming the -² is just typo then we can solve for x by substituting f(x) = -3
into the expression of f(x) = 3x² - 5x
3x² - 5x = -3
3x² - 5
Three friends went to the movies. They shared 4/5 of a candy bar. If they share the bar equally, how much of the candy bar will each person get?
The candy bar will each person get will be 4 / 15.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that three friends went to the movies. They shared 4/5 of a candy bar. If they share the bar equally.
The amount of candy shared by each person will be,
Amount = ( 4 / 5 ) ÷ 3
Amount = 4 / 15
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This subtraction represents a translation of the
given triangle
——- and ——-
Answer:
right 2 unitsdown 4 unitsStep-by-step explanation:
You want to know the translation effected by subtracting -2 from the x-coordinate, and subtracting -4 from the y-coordinate of the vertices of a triangle.
TranslationYou have correctly observed that the triangle vertex (-2, 0) is translated to (0, -4) by the subtraction of the translation matrix. That is, the x-coordinate is increased by 2, moving the point 2 units to the right, while the y-coordinate is decreased by 4, moving the point 4 units down.
The translation is to the right by 2 units, and a translation down by 4 units.
Answer: 2 units right 4 units down
Step-by-step explanation: trust
Simplify. -15 times the square root of y^2 if y>0
Answer:
-15y
Step-by-step explanation:
The square root of any squared number is always the number itself.
So in this case, it is -15y
Brainliest please. It'll help a lot.
Answer:
- 15y---------------------------------
Simplify the expression:
[tex]-15\sqrt{y^2}[/tex]We know the square root is never negative and since y is positive, we get:
[tex]-15\sqrt{y^2} =-15y[/tex]a line has a slope of 7/10 and a y intercept of (0,-4) what is the equation of the line in standard form
Considering the definition of a line, the equation of the line in standard form is y - 7/10x= -4
What is Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.The standard form of a linear equation is Ax + By = C. In this type of equation, x and y are variables and A, B, and C are integers.
Equation in this caseIn this case, you know:
A line has a slope of 7/10.A line has a y-intercept of (0,-4).So, the line can be expressed as:
y=7/10x -4
Expresed in standard form:
y - 7/10x= -4
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what fraction is 40 minutes of 8 hours
40 minutes of 8 hours as a fraction is 1/12.
What is fraction?Fractions represent the parts of a whole or collection of objects. A fraction has two parts namely numerator (upper part) and denominator (lower part).
Given are 40 minutes to 8 hours.
We can write -
(40 minutes/8 hours)
{40 minutes/(8 x 60)}
(40/480)
1/12
Therefore, 40 minutes of 8 hours as a fraction is 1/12.
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(30 points) write the equation of line a that goes through points (3,2) and has a y-intercept of 1
Use the equation that you wrote for line a to write an equation for line b which is perpendicular to line 8 and goes through the point (-4,2)
To write the equation of a line that goes through the point (3,2) and has a y-intercept of 1, we can use the point-slope form of a line. The point-slope form is:
y - y1 = m(x - x1)
Where (x1, y1) is a point on the line, and m is the slope of the line. The slope is a measure of the steepness of the line, and it is calculated as the rise (the change in y) over the run (the change in x).
To find the slope of the line, we can use the two points (3,2) and (3,1). The rise is 1 - 2 = -1 and the run is 3 - 3 = 0, so the slope is -1/0, which is undefined. This means that the line is a vertical line and does not have a slope.
Since the line is a vertical line, we cannot use the point-slope form to write its equation. Instead, we can use the slope-intercept form, which is:
y = mx + b
Where m is the slope of the line and b is the y-intercept. In this case, the slope is 0 (since the line is vertical), and the y-intercept is 1, so the equation of the line is:
y = 0x + 1
To write the equation of a line that is perpendicular to line a and goes through the point (-4,2), we need to find the slope of line a. Since line a is a vertical line, its slope is undefined. However, we know that the slope of a line perpendicular to it must be 0.
Using the point-slope form, the equation of line b is:
y - 2 = 0(x - (-4))
Simplifying, we get:
y = 0x + 2
So, the equation of line b is:
y = 0x + 2
How do I solve this system of equations using the elimination method
y=3x+13
2x=y-9
The value of x is -4 and the value of y is 1.
What is the value of x and y?In order to use the elimination method, rearrange the given linear equations.
y - 3x = 13 equation 1
y - 2x = 9 equation 2
Subtract equation 2 from equation 1:
-x = 4
x = -4
Substitute for x in equation 2
y - 2(-4) = 9
y + 8 = 9
y = 9 - 8
y = 1
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